Neuromorphic computing mimicking the functionalities of mammalian brain holds the promise for cognitive capabilities enabling new intelligent applications. However, research efforts so far mainly focused on using analog and digital CMOS technologies to emulate neural activities, and are yet to achieve expected benefits. They suffer from limited scalability, density overhead, interconnection bottleneck and power consumption related constraints. In this paper, we present a transformative approach for neuromorphic computing with Wave Interference Functions (WIF). This is a framework using emerging nonequilibrium wave phenomenon such as spin waves. WIF leverages inherent wave attributes for multidimensional, multivalued data representation and communication, resulting in reduced connectivity requirements and efficient neural function implementations. It also yields a compact implementation of an artificial neuron. Moreover, since WIF computation and communication are in the spin domain, extremely low-power operation is possible. Our evaluations indicate upto 57× higher density, 775× lower power and 2× better performance when compared to an equivalent 8-bit 45-nm CMOS neuron. Our scalability study using arithmetic circuits for higher bit-width neuron implementations indicate upto 63× density, 884× power and 3× performance benefits in comparison to a 32-bit CMOS equivalent design at 45 nm.